k-Wave

1. benji
   

   Member
   Joined: Dec '15
   Posts: 14

   hi,
   I am trying to add attenuation to a hetroginious soft tissue model.
   as a first step i have allocated a homoginious attenuation coefficient to the hole model:
   medium.alpha_coeff=a*ones(Nx,Ny,Nz);
   medium.alpha_power=1.02;
   medium.alpha_mode = 'no_dispersion';

   i am observing the next (unexpected) behaviour:

   1. for attenuation levels greater than 3db/(cm*MHz) - the simulation is unstable and pressure goes to infinity.

   2. when attenuation levels are less or equal to 3db/(cm*MHz) :
   a. the measured signal starts earlier (as if the wave propagates faster, but the speed in
   defined for the medium is exactly the same). as bigger the attenuation is, the faster it
   "arrives" the
   sensor.
   b. it seems as if the signal is being expanded in time axis (meaning p(a*t)) - and
   analogiously squeezed in frequency domain.
   c. the signal becomes not causal, and is not exactly zero in times before the signal arrives
   the sensor.

   I would really appriciate your help understanding the above phenomena. i expected having some dispersion, with every frequency attenuatted according to a*x[cm]*f[MHz], but that behviour is different.

   could i count on phase accuracy of the simulation to measure phase differance between different points?

   thank u very much for your kind help

   benji

   Posted 8 years ago #

2. benji
   

   Member
   Joined: Dec '15
   Posts: 14

   hi again,
   after experimenting a little more, here are some more details:
   1. the simulation is stable for alpha_power>1.05 or alpha_power<0.9 (also for alpha_coeff greater than 3dB)
   2. the recorded pressure signal measured is delayed for alpha_power<1, and exibits a negative delay for alpha_power greater than 1 (delay is relative to the signal measured without attenuation, but the same medium otherwise).as alpha_power is bigger (than 1) - so does the delay (and opposite when alpha_power<1).
   3. the signal is still expanded in time domain (why?)
   4. the signal becomes not casual as alpha_power becomes smaller (or bigger) than 1.
   5. defining: medium.alpha_mode = 'no_dispersion', makes no differance to the simulation! i get exactly the same results with and without it. also with that line, i observe a loss obeying the relation: a*x[cm]*f^b

   thank u
   benji

   Posted 8 years ago #

3. Bradley Treeby
   

   Developer
   Joined: Mar '10
   Posts: 1,643

   Hi benji,

   If you're using kspaceFirstOrder3D, the simulation will not be unconditionally stable when you add absorption. You can use the function checkStability to check if the time step is small enough to ensure stability.

   There is a also small phase error that is introduced when using kspaceFirstOrder3D due to the way the absorption term is implemented (see the k-Wave manual and the Modelling Power Law Absorption Example for more details). This can be counteracted by reducing the size of the time step.

   As an alternative, you can use kspaceSecondOrder. This is restricted to homogeneous media, but is unconditionally stable and encodes the absorption operator exactly.

   Three things to check:

   (1) Do you get the same results if your halve the time step (i.e., have you performed a convergence check)?

   (2) Do you seem the same behaviour if you use kspaceSecondOrder?

   (3) If you open the Modelling Power Law Absorption Example, set example_number = 3 and then run the simulations with and without medium.alpha_mode = 'no_dispersion', do you see any difference in the output?

   Brad.

   Posted 8 years ago #

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